On D4t-Cocyclic Hadamard Matrices
In this paper, we describe some necessary and sufficient conditions for a set of coboundaries to yield a cocyclic Hadamard matrix over the dihedral group D4t. Using this characterization, new classification results for certain cohomology classes of cocycles over D4t are obtained, extending existing...
| Autores: | , , , , , |
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| Formato: | artículo |
| Estado: | Versión enviada para evaluación y publicación |
| Fecha de publicación: | 2016 |
| País: | España |
| Recursos: | Universidad de Sevilla (US) |
| Repositorio: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/114849 |
| Acesso em linha: | https://hdl.handle.net/11441/114849 https://doi.org/10.1002/jcd.21510 |
| Access Level: | acceso abierto |
| Palavra-chave: | Hadamard matrix Ito’s type Q Hadamard matrix shift equivalence |
| Resumo: | In this paper, we describe some necessary and sufficient conditions for a set of coboundaries to yield a cocyclic Hadamard matrix over the dihedral group D4t. Using this characterization, new classification results for certain cohomology classes of cocycles over D4t are obtained, extending existing exhaustive calculations for cocyclic Hadamard matrices over D4t from order 36 to order 44. We also define some transformations over coboundaries, which preserve orthogonality of D4t -cocycles. These transformations are shown to correspond to Horadam’s bundle equivalence operations enriched with duals of cocycles. |
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